Related papers: Dynamics-Adapted Cone Kernels
Human brains respond to semantic features of presented stimuli with different neurons. It is then curious whether modern deep neural networks admit a similar behavior pattern. Specifically, this paper finds a small cluster of neurons in a…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
Helioseismic inferences of large-scale flows in the solar interior necessitate accounting for the curvature of the Sun, both in interpreting systematic trends introduced in measurements as well as the sensitivity kernel that relates…
Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal…
We propose kernel-gradient drifting, a one-step generative modeling framework that replaces the fixed Euclidean displacement direction in drifting models with directions induced by the kernel itself. Standard drifting is attractive because…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In \emph{Kernelized Diffusion Maps} (KDM), the kernel determines the accuracy of the RKHS estimator of a diffusion-type operator and hence the quality…
The relative balance between physics and data within any physics-informed machine learner is an important modelling consideration to ensure that the benefits of both physics and data-based approaches are maximised. An over reliance on…
Recent efforts have shown machine learning to be useful for the prediction of nonlinear fluid dynamics. Predictive accuracy is often a central motivation for employing neural networks, but the pattern recognition central to the network…
Convolutional networks are not aware of an object's geometric variations, which leads to inefficient utilization of model and data capacity. To overcome this issue, recent works on deformation modeling seek to spatially reconfigure the data…
In this paper, we describe Fourier-based Wave Front Sensors (WFS) as linear integral operators, characterized by their Kernel. In a first part, we derive the dependency of this quantity with respect to the WFS's optical parameters: pupil…
We introduce a new class of nonparametric prior distributions on the space of continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose…
A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves…
We discuss the physical properties and accuracy of three distinct dynamical (ie, frequency-dependent) kernels for the computation of optical excitations within linear response theory: i) an a priori built kernel inspired by the dressed…
Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstractions. It has proven effective for manifold learning, denoising, clustering, and visualization of…
Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…
Kernels are often developed and used as implicit mapping functions that show impressive predictive power due to their high-dimensional feature space representations. In this study, we gradually construct a series of simple feature maps that…
Unlike images which are represented in regular dense grids, 3D point clouds are irregular and unordered, hence applying convolution on them can be difficult. In this paper, we extend the dynamic filter to a new convolution operation, named…
We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…
Frequency dynamic convolution (FDY conv) has shown the state-of-the-art performance in sound event detection (SED) using frequency-adaptive kernels obtained by frequency-varying combination of basis kernels. However, FDY conv lacks an…